Voters in England and Wales went to the polls today to elect new county councils in what was seen here as the first test of the policies and popularity of Conservative Prime Minister Margaret Thatcher's government since its landslide victory in the 1983 general elections.

On their own terms, the races for thousands of seats on the governing bodies of the 47 counties are considered of little importance. Polls did not close until 9 p.m., and final results will not be tallied until Friday.

But much has happened in British politics since Thatcher transformed the 1982 military victory in the Falklands War against Argentina into an overwhelming electoral one the following year.

Unemployment continues to run at record levels of more than 13 percent. Although the government recently has displayed positive indices to show that its hands-off economic policies are working, figures coincidentally released today indicated a slight increase in the number of persons out of work during April.

At the same time, the opposition Labor Party has argued, with some apparent success, that sharp local tax increases have been the product of Thatcher cuts in central government contributions to local services, which, despite the new tax rates, have worsened.

Labor is betting that recent public opinion polls showing that it has pulled ahead of the Conservatives with a backing of 38 percent compared with the Conservatives' 33 percent, according to figures published last weekend, reflect a general disenchantment with both the often abrasive style and substance of six years of Thatcher rule. Today's vote, Labor leader Neil Kinnock said, would be "another landmark" in the party's return to voter favor after the disaster of 1983.

The opposition is not necessarily looking for majority control within the governing bodies of the 39 English and eight Welsh counties. What it hopes is to hold on to the gains it made in its own landslide victory in 1981, when these local seats last were contested.

Despite the new national opinion polls, however, a number of factors are working against that prospect. Many of the counties in question are traditionally Conservative strongholds. Thatcher supporters believe that the large number of seats they lost in 1981 -- while still maintaining an overall majority -- were the victims of a midterm slump during her first government and predated the Falklands War.

Additionally, there are no elections in the London boroughs or municipal councils of five other A key factor is the role of the centrist alliance. large cities, where Labor long has held sway. The government has proposed abolishing those councils by early next year, and their current makeup is being maintained pending the outcome of that abolition effort. There also are no elections today in Scotland or Northern Ireland.

The real question, however, revolves around the performance of Britain's third large political group, the alliance composed of the Liberal and Social Democratic parties.

The Liberals traditionally have done rather poorly in gaining control of councils through these local races, and the newly formed Social Democrats were just coming into existence in 1981 and did not contest the council seats.

But with a steady climb in the polls since last year, the centrist alliance now commands at least 28 percent of the national vote, much of it in the rural county areas.

Conventional wisdom has been that most of the alliance's popularity so far has been pared from the Labor Party, whose leadership was hurt by the Falklands factor and has spent much of the last two years mired in internecine battles and in support of unpopular labor union causes.

Thus, political commentators noted on the eve of today's vote, Labor's true enemy in the council races is the alliance, which ultimately hopes to replace it as the formal opposition party.

Having taken nearly all the voter support it hopes to get from Labor, the alliance hopes in today's vote to hold Labor static and begin to take some of the Conservatives' share.

When the votes are counted, an alliance statement said yesterday, "if there are majority councils at all, Conservatives will be in control by no more than a few seats."

Overall, wrote London Times political editor Julian Haviland today, "these elections are the best chance for the next 12 months for Labor to establish itself as the government's only serious challenger, as the national polls are suggesting. It cannot afford to fail, and the alliance parties cannot let it succeed."